#/usr/bin/perl

use strict;
use warnings;

my $string = 'NOT ("test(s)"[MESH] AND ("A"[MESH] OR "B"[MESH]))';

my $parens_guts;  # Can't combine this line with the next one.
$parens_guts = qr/
   (?:
      "[^"]*"
   |
      \(  (??{ $parens_guts })  \)
   |
      [^"()]
   )*
/sx;

$string =~ s/
   \s* NOT \s*
   (?:
      "[^"]*"\[MESH\]
   |
      \(  (??{ $parens_guts })  \)
   )
//gsx;

print("[$string]$/");